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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
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Seeking very regular $\mathbb Q$-acyclic complexes
This question was raised from a project with Nati Linial and Yuval Peled
We are seeking a $3$-dimensional simplicial complex $K$ on $12$ vertices with the following properties
a) $K$ has a complete …